In recent years, for fuel reduction or exhaust gas reduction, an idling stop device for automatically stop/activate an engine of a vehicle during a stop of the vehicle for a relatively short time such as waiting at a stoplight has been put to practical use. For example, according to a vehicle having an idling stop device disclosed in Japanese Unexamined Patent Application Publication No. 2009-13953, if a stopping condition is satisfied, that is, if a brake is stepped on during a traveling state of the vehicle and the vehicle becomes in a stop state, an engine is automatically stopped, while if an activation condition is satisfied, that is, if the brake is released during the stop of the engine, the engine is automatically activated.